STATICS As shown in the picture, a weight W is attached to a metal pole by a thi
ID: 1576272 • Letter: S
Question
STATICS
As shown in the picture, a weight W is attached to a metal pole by a thin cord hanging over a massless, frictionless pulley attached to the pole 40.0 cm below the top. The pole is 1.75 meters tall, weighs 55.0 N and has a hinge at its base. It is connected to the wall using a thin wire that runs from the top of the pole to a lower point on the wall. The nail that holds this wire to the wall will pull out if it experiences an outward force greater than 22.0 N.
a. What is the greatest weight W that can be supported by this apparatus without pulling out the nail?
b. What is the magnitude of the force that the hinge exerts on the pole?
37.0 HingeExplanation / Answer
a)
As the pole is in equilinrium net force and net torque acting on it mujst be zero.
Apply net torque about hinge = 0
W*(1.75 - 0.4) - T_max*1.75*sin(37) = 0
W*1.35 - 22*1.75*sin(37) = 0
W = 22*1.75*sin(37)/1.35
= 17.2 N
b) let Fx and Fy are the components of force exerted by hinge on the pole.
Aply, Fnetx = 0
Fx - W = 0
Fx = W = 17.2 N
Apply, Fnety = 0
Fy - 55 - 22*cos(27) = 0
Fy = 55 + 22*cos(27)
= 74.6 N
so, F_hinge = sqrt(Fx^2 + Fy^2)
= sqrt(17.2^2 + 74.6^2)
= 76.6 N
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